Friday, February 01, 2008

Arnauld suggests that Malebranche's epistemology can be summarized in three points:

The first is that our mind can see material things not through themselves, but only through representative beings which are distinct from our perceptions and must precede them, and to which he gave the name 'ideas,' though it was a misuse of the word.

The second is that our mind can find those ideas, or beings representative of material things, only in God.

The third is that what makes it possible for the mind to find them in God is that God contains in himself an infinite intelligible extension.

Antoine Arnauld, On True and False Ideas, Kremer, tr. Edwin Mellen (1990) p. 106. The summary is fairly decent, as one would expect of Arnauld, although one can quibble a bit with both the selection and the unqualified statements.

I previously noted a supposition that allows subalternation without any bothering with existential import; discussing the matter with Tom, I said at one point that I didn't know if the particular supposition I noted was required. Having thought about the matter more, I can think of the following distinct suppositions that allow for subalternation.

(1) A and I as having existential import. Whatever it means to attribute existential import to propositions, it's generally taken for granted that attributing it to A and I allows subalternation. Similarly for E and O.

(2) Some S is S. Whether we take "Some S is S" as existential or not, it still makes supposition possible:

-S+P+S+STherefore +S+P

-S-P+S+STherefore +S-P

(3) A propositions as double propositions. Lewis Carroll allows subalternation in his system by making A propositions double propositions: "All S is P" simply means "Some S is P and No S is nonP." (He also accepts that A and I have existential import. But I don't see that this is strictly required by the move; Carroll accepts existential import for A and I for independent reasons.) Welton also has this view, and suggests the same for E propositions.

(4) Instantiation with generalization. We can add to term logic forms of instantiation and generalization:

Start with -S+P (All S is P, i.e., every instance of S is P)instantiate to *S+P (a given instance of S is P)generalize to +S+P (Some S is P).

Whether you think this fourth supposition is a case of 'existential import' depends, I think, on what you think something like universal instantiation is in the predicate calculus.

I'm sure there are others that could be put forward.

UPDATE: Doing a bit of reading, I find that Carveth Read claims that subalternation follows merely by the principle of identity; McCosh says it follows from the principle that "whatever is true of a class is true of any and of each of the members of the class." I think Read means same thing as McCosh; Veitch also claims subalternation rests on the principle of "Identity of whole and part". Morell likewise says that the correctness of subalternation "depends upon the relation which a logical whole bears to its parts." Parimal Kumar Ray gives two arguments for subalternation: (1) the particular simply repeats (part of) the information in the universal; and (2) what fails even in one case cannot be universally affirmed and what obtains even in one case cannot be universally denied. Francis Garden just says that it is "plain to the dullest capacity."

Monday, January 28, 2008

Not only is it St. Thomas day in the West, it is the memorial of St. Ephrem in the East. And as I've said often enough, you can never have too many calendars giving you things to celebrate (for private purposes, anyway).

On a certain day a pearl did I take up, my brethren;I saw in it mysteries pertaining to the Kingdom;Semblances and types of the Majesty; It became a fountain, and I drank out of it mysteries of the Son.

I put it, my brethren, upon the palm of my hand,That I might examine it: I went to look at it on one side, And it proved faces on all sides.

I found out that the Son was incomprehensible, Since He is wholly Light. In its brightness I beheld the Bright One Who cannot be clouded,And in its pureness a great mystery, Even the Body of Our Lord which is well-refined: In its undivideness I saw the Truth Which is undivided.

It was so that I saw there its pure conception, The Church, and the Son within her. The cloud was the likeness of her that bare Him, And her type the heaven, Since there shone forth from her His gracious Shining.

I saw therein his Trophies, and His victories, and His crowns. I saw His helpful and overflowing graces, And His hidden things with His revealed things.

I had intended to blog on this way back in December, but forgot; being the memorial for Thomas Aquinas, this is a good day to make up for that. Among Thomas's extant sermons is one, usually known by the name Inveni David, which is devoted to St. Nicholas of Myra. The exact circumstances of the sermon are unknown, but we know that it was preached in December in Paris either on St. Nicholas Day or around that time. This essay (PDF) by Peter Kwasniewski does a good job of giving the background. You can find the sermon here.

The topic of the sermon is that God works wonders in His saints, and St. Thomas treats of this topic by taking a verse from the Psalms about David:

I have discovered David my servant; with my holy oil I have anointed him;my hand will help him, and my arm will strengthen him (Ps. 88:21-22).

This gives us a series of wonders that God works in the servants of God -- David in particular, of course, but also any servant of God. And thus Thomas uses it to speak of how St. Nicholas was such a servant. There are four basic parts to the verse, to which Aquinas assigns one feature of God's wondrous working in the saints:

(1) I have discovered David my servant: election(2) with my holy oil I have anointed him: consecration(3) my hand will help him: execution of duties(4) and my arm with strengthen him: steadfastness

Thus Thomas will show wondrous election, singular consecration, effective execution of office, and abiding steadfastness in St. Nicholas. Actually, he never gets to the last; the sermon we have stops abruptly and without explanation after (3).

Wondrous Election

I have discovered David my servant, the Psalmist says; what's involved in discovering someone? Discovery, says Thomas, suggests rarity, at least to the extent that it needs to be discovered; it suggests search; it suggests disclosure; and it suggests conviction through experience. All these are elements of God's wonderful choosing of St. Nicholas: the first in that St. Nicholas was virtuous from youth, the second in that the Lord seeks faithful souls to delight in; the third in that Nicholas stood out through his pious affection and profound mercy and compassion; and the fourth in that Nicholas faithfully served the Lord's interests rather than his own. The third is particularly important for Aquinas; St. Nicholas is an example he holds up in more than one place for his compassion and mercy. He clearly likes the story of St. Nicholas finding a way to give gold in secret to the poor virgins so that they could have a dowry without the embarrassment of being beholden to him for it. Notably Thomas also uses his discussion of Nicholas's election to attack abuses by the clergy.

Singular Consecration

According to legend, St. Nicholas was elevated to the position of bishop by God Himself. The old bishop had died with no one obvious as a replacement. Those who were trusted with choosing the successor had a dream one night that they should consecrate as bishop the first man who walked through the door of the Church that morning. This happened to be Nicholas, who was at the time a young priest and a newcomer to Myra. He took considerable convincing, but eventually he was installed as bishop. This is perhaps subtly in the background here, although Aquinas doesn't mention it explicitly here (he does explicitly mention it elsewhere, so he knew of the story). Instead he focuses on the phrase with my holy oil I have anointed him. Oil has four uses, says Aquinas, all of which are suggested in this context.

First, oil is used for healing. Thus oil is an image of God's healing grace, and we see the operation of such grace in such a holy man as Nicholas.

Second, oil is used for lighting. To this extent it symbolizes the learning of wisdom, which is why it is associated with prophecy and illumination.

Third, oil is used for flavoring. In this sense it is an image of spiritual joy; just as a sprinkling of oil makes food taste better, so does a sprinkling of spiritual joy make good works easier. It is in this sense that oil is associated with priesthood.

Fourth, oil is used for softening and smoothing. Understood in this way it signifies mercy and kindness of heart which, of course, St. Nicholas had in astounding measure. Thus, says Thomas Aquinas, just as oil spreads itself out, so does mercy, and just as oil coats things, so mercy coats every good work. He then has a very interesting passage:

You ought to consider that in the future, according to the merits of graces the evidence of rewards will appear in the glorified bodies of the saints, and that even in this life the signs of their affection appear. This is evident in the case of blessed Francis, where the signs of the passion of Christ became visible, so vehemently was he affected by the passion of Christ. In blessed Nicholas's case, signs of mercy appeared when "his tomb sweated oil," thus indicating that he was a man of great mercy.

The linking of the two extremely popular saints, Saint Francis and Saint Nicholas, is rather interesting in itself, since, while Nicholas founded no order, there are nonetheless a great many similarities between the two, as regards their place in the Church and what they have left for posterity. It has also not gone without notice that here Thomas the Dominican takes explicit trouble to mention the stigmata of Saint Francis, which has suggested to some that his audience may have been Franciscan.

In any case, Thomas holds that this fourth signification of oil is why oil is often associated with kingship.

And thus in these four ways, divine grace, prophetic wisdom, priestly gladness, and kingly compassion, God works wonders in His saints.

Effective Execution

My hand shall help him. The hand symbolizes God's strength, and Thomas suggests four ways in which God's strength is found to operate in saints like Nicholas. First, God drew Nicholas to Himself and away from evil. Second, God guided Nicholas as He does all the just. Third, He gave him strength and comfort. And fourth, because Nicholas showed exquisite mercy, God worked miracles through him.

And this is how the sermon ends, abruptly but memorably:

It was mercy that made blessed Nicholas an extraordinary man, and the Lord strengthened him even unto everlasting life. May He lead us there, who lives with the Father and the Holy Spirit, &c.

You know there is a conclusion of some sort to be drawn when reading over what you've written for a paper you suddenly come across the brief passage you just wrote five minutes ago and find that it has half a dozen typos and a sentence that makes no sense whatsoever....

Sunday, January 27, 2008

You are struck by a vision, some exquisite example of beauty. Being struck, you are changed, this beautiful object introducing itself into your very disposition, so that you become, so to speak, adapted to it, so as to find satisfaction in it. You are pleased by it, and, being pleased by it, you desire it, and this desire seeks the joy and rest of its presence. Thus you have become caught up in a sort of circle: it has joined itself to you, by changing you; you are thereby driven to join yourself to it, that you may rejoice in it. You are set in motion by it, and this motion comes to rest only in that which started the motion in the first place.

Such is Thomas Aquinas's view of the passion of love. In this account, the experience of love consists in a series of changes induced in us, immutationes, the first of which, complacentia, the taking pleasure in, or being pleased by, a thing, is what we most often refer to as 'love'. The beloved becomes, in a sense, a part of the lover. But this complacentia isn't the term of the change; it continues on to desiderium, desire, the drive to union (of some sort) with what is loved, and the change involved in this desire continues until one finds a way to be united to what is loved, and rest in it. This rest is gaudium, joy.

This is all on the supposition that everything else is equal, of course; any discussion of the changes involved in the passions has a mercurial and unstable subject. There are endless numbers of things that might intervene. But there is enough pattern to the chaos that each of these, the amor or complacentia, the desiderium, the gaudium, is a recognizable feature, as is the sense of coaptatio, adaptation to the beloved, the experience of being disposed by the loved one to the loved one.

There is much more to St. Thomas's account of the passion than this; his discussion of the effects of love is particularly interesting. Love, says Thomas, has four proximate effects: liquefactio, fruitio, languor, fervor. In liquefactio our defenses are melted, our heart is softened; to the extent the beloved is present to us, we have fruitio, enjoyment; to the extent the beloved is absent, we have languor, sorrow or pining, and fervor, the passion to possess. These effects are induced in us proportional to the severity of the immutatio. Beyond this there are other effects that may ensue: union, indwelling (dwelling upon the beloved in thought and in sympathy), zeal or jealousy (understood as the repulsing of what stands in love's way), ecstasy (in the sense of being somehow carried away, either elevated beyond or debased below our usual state of sanity), and the myriad acts of lovers.

How many men are fallen, sons of men,how many dead and dyingin great Ascalon and Tyre?How many widows cryingwhere blood flows down like waterfrom a horse's smashing hoof?

How many youths lie dead, O sons of men?How many in the grave unwed,where roses grow, and poppies,on the bloody fields of war?How many, O ye nations?How many slip to darkness,each face to be seen no more?How many men are fallen, sons of men?

In starlit skies, brightly shining,Mars has wandered to work his will;the wolves on the plain are howling,crows and vultures take their fill.

The formless hand its word has written;read, O men, the script as bidden,a word, a pang, a question:We see it in gilded fireon those blessed, familiar places,the children's heads in play,on their foreheads and on their faces:"Quick pickings and easy prey".

An angel in heaven was flyingto and fro o'er all the earth;an angel in loud voice crying,"How many, O sons of men?"

Looking for something else I came across this excellent little passage:

Astrology, to cite but one example, is frequently cast in the role of an outmoded competitor to modern astronomy. This is a misunderstanding of the function that astrology plays in people’s lives. Astronomy is about planets, stars, and galaxies; astrology, however, is about me, and the special place I have in the grand cosmic scheme. It explains my unique personality, my special hopes and desires. From astronomy I learn that I am but an insignificant creature in some minor corner of the universe; astrology tells me I am someone unique and important. In this respect, astrology does not function as an alternative to scientific astronomy, but as a rival to the personal support provided by religion.

Some rought thoughts on the matter. Hartley Slater famously argued that paraconsistent negation, such that (p & ~p) does not 'explode' or imply everything, was really just a subcontrariety operator and therefore to be distinguished from the more robust negation in which (p & ~p) is a contradiction. Slater uses this to argue that really there is no such thing as paraconsistent logic; others, Béziau comes to mind, have taken the same point to argue that even classical logic has paraconsistent elements. In any case, one response to Slater I've occasionally come across is to argue that there is no significant sense in which paraconsistent negation is subcontrariety, or that, at most, there is just a vague analogy between paraconsistent negation and subcontrariety. But it's easy enough to show that some paraconsistent negation really is nothing other than subcontrariety.

As I've noted before, it is possible to handle all of standard propositional logic in terms of categorical propositions if you make two assumptions:

(1) Propositions are terms;(2) The universe of discourse is singleton.

As it turns out, it is (2) that makes negation function standardly for this propositional logic. You can create a system where negation is paraconsistent if you reject (2) and add the following two assumptions to the list:

(2') The universe of discourse is plural;(3') The default interpretation of propositions is particular.

Thus, 'p' is interpreted as +D+P (something in the domain is P); ~p is interpreted as +D-P (something in the domain is not P). With (2) universals can be inferred from particulars; which means that these two cannot both be false (as particulars) and cannot both be true (as implying universals), and therefore are contradictory. When we reject (2) however, the particulars no longer warrant inference to their universal counterparts; we no longer have a term logic of one individual. Thus (p & ~p) can be true with no ill effects; the negation is an opposition of quality between two particular affirmatives and therefore subcontrariety.

This is not, I think, the only possible way to get paraconsistent negation, so I think Slater's argument fails to the extent it is taken to apply to all forms of it. But it is important to realize that

(a) this negation is paraconsistent;(b) this negation is literally subcontrariety, not merely analogous to it.

This point is related to another. I mentioned that Béziau and others have taken Slater's interesting comment about subcontrariety in another direction, arguing that you can have paraconsistent negations in classical logics. For instance, the not-necessary operator is read as paraconsistent, and its place on the modal square of opposition clearly connects it to subcontrariety. Suppose we were to take the above categorical approach to propositional logic, the one that accepts (2'). This breaks from standard propositional logic and allows paraconsistent negation. But I haven't said much about how propositions should be interpreted in this approach, except to say that they are particular and in a non-singleton universe. Suppose we understood them in thise way: the domain of discourse is possible worlds or, if you prefer, possible states of the world. Then the paraconsistent negation turns out to be nothing other than the modal version that others have suggested.

Very similar things could be said if you were looking for a paracomplete logic; paracompleteness bearing much the same relation to contrariety as paraconsistency to subcontrariety.

Caveats

For a rough introduction to my philosophy of blogging, including the Code of Amiability I try to follow on this weblog, please read my fifth anniversary post. I consider blogging to be a very informal type of publishing - like putting up thoughts on your door with a note asking for comments. Nothing in this weblog is done rigorously: it's a forum to let my mind be unruly, a place for jottings and first impressions. Because I consider posts here to be 'literary seedings' rather than finished products, nothing here should be taken as if it were anything more than an attempt to rough out some basic thoughts on various issues. Learning to look at any topic philosophically requires, I think, jumping right in, even knowing that you might be making a fool of yourelf; so that's what I do. My primary interest in most topics is the flow and structure of reasoning they involve rather than their actual conclusions, so most of my posts are about that. If, however, you find me making a clear factual error, let me know; blogging is a great way to get rid of misconceptions.